# There Are Two Identical Firms Eqt Corp And Dbt Corp Except For Their capital structure

There are two identical firms EQT Corp and DBT Corp except for their capital structure. For example none of the firms pay taxes, and earnings are \$22,000 per year. There is no growth for any of the firms, i.e., they pay out all earnings to shareholders as dividends. EQT is an all equity firm with 1,000 shares outstanding. In contrast, DBT has \$40,000 worth of debt outstanding with interest rate of 10%. The equity price of DBT Corp is \$120 with 500 shares outstanding.

(a) What is the equity value of EQT Corp? And, what is EQT’s stock price?

(b) What are the expected returns on equity of each firm? Which company is riskier and why?

(c) Suppose currently you own 300 shares of EQT stock and John owns 200 shares of DBT stock. What would you do if you want to have exactly the same total dividends as John’s? Assume you can borrow or lend at 10%.

2. Carlson Enterprise is financed entirely by common stock with a beta of 0.8. The stock is currently traded at \$100 per share. There are no taxes. The stock is expected to have constant earnings in perpetuity, has a price- earning multiple of 16. The market expected return is 12%. The company decides to repurchase one third of its common stock and substitute with an equal value of debt. If the debt yields the same as the risk-free rate of 4%, calculate:

(a) the beta of the common stock after the refinancing

(b) the required return and risk premium on the common stock before and after the refinancing

(c) the required return on the company (i.e., stock and debt combined) after the refinancingAssume that the EBIT of the firm is expected to remain constant in perpetuity.

Determine:

(d) the percentage increase in earnings per share after refinancing

(e) the new price-earnings multiple3. Backyard Utility is expected to have an EBIT of \$250,000 and is an all-equity firm. EBIT is expected to grow at 6% per year. In order to get this growth rate, Backyard needs to retain 50% of earnings for investment. The remaining will be paid out as dividends. The firm’s corporate tax rate is 20%. The discount rate for the firm is 10%.

(a) What is the market value of the firm?

(b) Now assume the firm issues \$1.5 million of debt paying interest of 5% per year, using the proceeds to retireequity. The debt is expected to be permanent. What is the equity value of the firm after refinancing?

(c) What is the required return on equity after refinancing?

(d) In order to get the same growth rate of 6%, Backyard only need to retain 29.41% of its earnings forinvestment. Compute the equity value by discounting all the future dividends as in (a).

(Hint: you shouldget the same result as in (b))(e) If Backyard’s manager only wants its total equity value to be \$1.7 million instead, how much debt shouldBackyard actually use?

4. APV Inc. is considering an investment project that will generate a level after-tax cash flow of \$235,000 a year for the next 5 years. The all-equity discount rate is 15%, and the project requires an investment of \$800,000.Should APV take on the project? Now, if the management desires to raise 50% of the initial investment in the form of debt at an interest rate of 8%. This debt is repaid in equal yearly installments; interest accrues on the unpaid balance. The corporation tax rate is 30%. What is the APV of the project?

5. Here is a simplified book balance sheet for Upjohn Company at the end of 2005 (dollars in millions):Current assetsNet property, plant,and equipment Other assets\$1,4181,240 472Current liabilities \$653 Long-term debt 457

(a) Calculate Upjohn’s WACC. Use the CAPM and the data above. Make additional assumptions and approximations as necessary. (hint: only use “Long-term debt” as debt)

(b) What would Upjohn’s WACC be if it moved to and maintained a debt to market value ratio of 20%? Assume the only taxes are corporate taxes.

(c) Assume that the bondholders and the equityholders have effective tax rates of 30% and 10%, respectively, and the current market price of \$25 reflects this capital structure. What would be the total equity value if Upjohn were 100% equity finance?

6. Managers of the Edge Corporation must choose between two mutually exclusive projects. Suppose that the project that Edge chooses will be the only business it does next year, and assume zero discount rate. Therefore, the payoff on the project will determine the value of the firm. Edge is obliged to make a \$500 payment to bondholders. The first project has low risk:State of the economy Slump Probability 0.3 Project Payoff 600Boom 0.7 700Low-risk ProjectDeferred taxes 199 Shareholders’ equity 1,821 Total 3,130 Total 3,130 Other information:There are 100 million shares outstanding with a per share price of \$25 at end of year. The company has a beta of 1.2. Historical average risk premium is 8.0% per year and the risk-free rate is 4%. Newly issued Upjohn long-term debt carries a spread of 1.0% to the risk-free rate. The company’s marginal tax rate is 30%.

If the firm does not undertake the low-risk project, it will choose the following high-risk project: High-risk Project

State of the economy ProbabilityProject PayoffSlump 0.3 100Boom 0.7 800

(a) Which project is the social optimum?

(b) Which project would be preferred by stockholders? Why?